Geometric Design (II)

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Geometric Design (II)
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Learning Objectives

• To calculate minimum radius of horizontal curve
• To understand design concepts for transition
  curves and compute min length
• To understand the role of SSD in horizontal and
  vertical design
• To define and apply grade considerations
• To develop vertical curves
• (Chapter 6.1 6.4)

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Horizontal Curve

• Minimum Curve Radius
• Curve requiring the most centripetal force for
  the given speed
• Given emax, umax, Vdesign

R
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Horizontal Curve Properties

• Based on circular curve
• R radius of curve
• D degree of curve
• ? central angle
• T length of tangent
• L length of curve
• LC long chord
• M middle ordinate dist
• E external dist

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Horizontal Design Iterations

• Design baseline
• Curve radius above the minimum
• Superelevation and side-friction factor not
  exceeding the maximum values
• Design is revised to consider
• cost, environmental impacts, sight distances,
  aesthetic consequences, etc. 

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Horizontal Curve Sight Distance

• Sight line is a chord of the circular curve
• Sight Distance is curve length measured along
  centerline of inside lane

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Horizontal Curve Sight Distance

• Figure 6-10

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Transition Curves

• Gradually changing the curvature from tangents to
  circular curves

Without Transition Curves
With Transition Curves
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Transition Curves

• Gradually changing the curvature from tangents to
  circular curves
• Use a spiral curve
• L min length of spiral (ft)
• V speed (mph)
• R curve radius (ft)
• C rate of increase of centrifugal accel
  (ft/sec3), 13

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Transitional Curves

• Gradually changing the cross-section of the
  roadway from normal to superelevated (Figure 6-9)

Keep water drainage in mind while considering all
of the available cross-section options
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Vertical Alignment
Reduced Speed
Increased Speed
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Vertical Alignment

• Grade
• measure of inclination or slope, rise over the
  run
• Cars negotiate 4-5 grades without significant
  speed reduction
• Trucks significant speed changes
• 5 increase on short descending grades
• 7 decrease on short ascending grades

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Grade Considerations

• Maximum grade depends on terrain type, road
  functional class, and design speed

Rural Arterials
Terrain 60mph 70mph
Level 3 3
Rolling 4 4
Mountainous 6 5
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Grade Considerations

• Critical length of grade
• Maximum length which a loaded truck can travel
  without unreasonable speed reduction
• Based on accident involvement rates with 10mph
  speed reduction as threshold

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Grade Considerations
General Design Speed Reduction
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Vertical Curves

• To provide transition between two grades
• Consider
• Drainage (rainfall)
• Driver safety (SSD)
• Driver comfort
• Use parabolic curves
• Crest vs Sag curves

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Vertical Curves
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Vertical Curves

• Given
• G1, G2 initial final grades in percent
• L curve length (horizontal distance)
• ? Develop the actual shape of the vertical curve

point of vertical intersection
PVI
point of verticaltangency
point of vertical curvature
G1
G2
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Vertical Curves

• Define curve so that PVI is at a horizontal
  distance of L/2 from PVC and PVT
• Provides constant rate of change of grade

A
G1
G2
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Example

• G1 2
• G2 -4
• Design speed 70 mph
• Is this a crest or sag curve?
• What is A?

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Vertical Curves

• Major control for safe operation is sight
  distance
• MSSD should be provided in all cases (use larger
  sight distance where economically and physically
  feasible)
• For sag curves, also concerned with driver
  comfort (large accelerations due to both
  gravitational and centrifugal forces)

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Crest Vertical Curves

• Critical length of curve, L, is where sight line
  is tangent to the crest
• Assume driver eye height (H1) 3.5 ft and object
  height (H2) 2.0 ft and SMSSD

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Sag VC - Design Criteria

• Headlight sight distance
• Rider comfort
• Drainage control
• Appearance

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